Step-by-step Solution

Solve the trigonometric equation $\frac{5^2-7^x}{\cos\left(\frac{\pi }{8}\right)}=\frac{9}{5}$

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Step-by-step explanation

Problem to solve:

$\frac{\left(5^2-7^x\right)}{cos\left(\frac{\pi}{8}\right)}=\frac{9}{5}$

Learn how to solve trigonometric equations problems step by step online.

$\frac{25-7^x}{\cos\left(\frac{\pi}{8}\right)}=\frac{9}{5}$

Unlock this full step-by-step solution!

Learn how to solve trigonometric equations problems step by step online. Solve the trigonometric equation (5^2-7^x)/(cos((3.141592653589793/8))=9/5. Calculate the power 5^2. Calculating the cosine of \frac{\pi}{8} degrees. Multiply both sides of the equation by 0.9239. We need to isolate the dependent variable x, we can do that by subtracting 25 from both sides of the equation.

Final Answer

$x=1.6188$

Problem Analysis

$\frac{\left(5^2-7^x\right)}{cos\left(\frac{\pi}{8}\right)}=\frac{9}{5}$

Time to solve it:

~ 0.05 seconds